Realistic electronic sound synthesis is becoming increasingly important, in part due to the rapid development of multimedia and virtual reality applications. Two traditional techniques for synthesizing music are frequency modulation (FM) synthesis and Wavetable (sample-and-play) synthesis. Generally, FM methods generate sounds using sinusoidal oscillators. Wavetable methods store sound segments produced by actual instruments and synthesize the instruments by playing back digitally processed sequences of the sound segments. Both FM and Wavetable sound synthesis systems have their drawbacks. For instance, although FM synthesis can produce a wide range of interesting sounds and Wavetable synthesis is able to produce tones having timbres close to that of musical instruments, both methods are deficient at producing the large dynamic sound range capable of being produced by acoustic instruments.
An alternate, more recent technique, for electronically synthesizing sound use, digital waveguide filters (DWFs). DWFs mathematically simulate, using a bi-directional delay line with modification filters, wave propagation on a plucked string. That is, DWFs physically model wave propagation occurring in the string. A number of patents and publications describe music synthesis using DWFs, including: U.S. Pat. No. 4,984,276 to Julius O. Smith; U.S. Pat. No. 5,212,334 to Julius O. Smith; U.S. Pat. No. 5,448,010 to Julius O. Smith; and the publication by Julius O. Smith, "Physical Modeling Using Digital Waveguides," Computer Music Journal, Vol. 16, No. 4, 1992. The contents of these three patents and the publication are incorporated by reference herein.
DWFs provide a "virtual string" that can authentically simulate the dynamics of a plucked string. However, DWF modeling requires a number of physical string parameters that are difficult to measure directly. For example, parameters describing the amount of energy loss (the energy loss constant) and traveling wave reflection (reflection coefficient) at any particular point in the string often must be determined by cumbersome trial-and-error methods.
There is, therefore, a need in the art to be able to synthesize sounds produced by a plucked string using a "virtual string" that can be modeled with easily obtainable parameters.